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From |
Jorge Eduardo Pérez Pérez <perez.jorge@ur.edu.co> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Testing homogeneity and symmetry in QAIDS model with bootstraped standard errors. |

Date |
Thu, 20 Jan 2011 01:32:46 -0500 |

Dear Statalist, I am estimating a Quadratic Almost Ideal Demands Sistem (QAIDS) as in Banks, Blundell and Lewbel (1997) (full reference at the end) I am aware of Brian Poi's routines to estimate this system via the -nlsur- command, but since I want to correct for endogeneity of total expenditure, I am using the Iterative Least Squares Estimator of Blundell and Robin (1999). Basically, I estimate a reduced form for total expenditure, then I use the estimated residuals as additional regressors in the share equations of the demand system. I want to account for heteroskedasticity and clustering in my data, so I am bootstrapping the standard errors. I want to test symmetry and homogeneity in my estimated system. An standard likelihood ratio test would not be valid in this case since the assumptions are not met. I have implemented two approaches to do this: 1. Carry out the bootstrap estimation and use -test- afterwards, i.e: bs, rep(1000) cluster(city) : ile test [share1]g11 + [share1]g12 + [share1]g13 + [share1]g14 + [share1]g15 + [share1]g16 + [share1]g17 = 0, notest test [share2]g21 + [share2]g22 + [share2]g23 + [share2]g24 + [share2]g25 + [share2]g26 + [share2]g27 = 0, notest accum .... test [share6]g61 + [share6]g62 + [share6]g63 + [share6]g64 + [share6]g65 + [share6]g66 + [share6]g67 = 0, accum where -ile- is my own command for the iterative least squares estimator. 2. Calculate a chi-squared statistic (again via -test-) in each step of the bootstrap, then test symmetry and homogeneity using the empirical distribution of the chi-squared statistics, i.e program define homtest, rclass ile test [share1]g11 + [share1]g12 + [share1]g13 + [share1]g14 + [share1]g15 + [share1]g16 + [share1]g17 = 0, notest test [share2]g21 + [share2]g22 + [share2]g23 + [share2]g24 + [share2]g25 + [share2]g26 + [share2]g27 = 0, notest accum .... test [share6]g61 + [share6]g62 + [share6]g63 + [share6]g64 + [share6]g65 + [share6]g66 + [share6]g67 = 0, accum return scalar chi=r(chi2) end bs chi=r(chi), rep(1000) cluster(city) saving(chi, replace): homtest matrix b=e(b) local chis=e(b)[1,1] use chi, clear quietly count if chi>`chis' display "p-value = " r(N)/_N These two approaches yield very different results. I am rejecting the null with the first approach, while not rejecting with the second approach. Which one is correct? I think, in the first approach, Stata is using the bootstrap estimate of the covariance matrix to compute the Wald test. In the second approach, Stata computes the Wald test using the OLS covariance matrix in each step. The only difference between these approaches should be some asymptotic refinement with the second approach, but I have more than 7000 observations, so they should be equivalent. Full references: BANKS, JAMES; BLUNDELL, RICHARD y LEWBEL, ARTHUR (1997). “Quadratic Engel Curves and Consumer Demand”. The Review of Economics and Statistics, 79(4),pp. 527–539. BLUNDELL, RICHARD y ROBIN, JEAN MARC (1999). “Estimation in Large and Disaggregated Demand Systems: An Estimator for Conditionally Linear Systems”. Journal of Applied Econometrics, 14(3), pp. 209–232. _______________________ Jorge Eduardo Pérez Pérez * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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